Can you please clarify

Prove that 3246(mod 11) = 3246(mod 3) + 3246(mod 5)

Well, , , . . QED.

By simply performing these calculations, it can be easily "proved." I do not see anything deeper in this problem. Any random numbers can be thrown together and possess such properties by pure coincidence. What exactly is it your teacher wants you to prove here? Or do you simply have to prove you know your modular arithmetic?